What is the derivative of y= 1/2 e^{2x}+e^x+1 ?

The derivative of y= 1/2 e^{2x}+e^x+1 is e^x+e^{2x}

What is the first derivative of y= 1/2 e^{2x}+e^x+1 ?

The first derivative of y= 1/2 e^{2x}+e^x+1 is e^x+e^{2x}

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derivative of

y = \frac{1}{2} e^{2 x} + e^{x} + 1

e^{x} + e^{2 x}

Solution steps

\frac{d}{d x} (\frac{1}{2} e^{2 x} + e^{x} + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{2} e^{2 x}) + \frac{d}{d x} (e^{x}) + \frac{d}{d x} (1)

\frac{d}{d x} (\frac{1}{2} e^{2 x}) = e^{2 x}

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (1) = 0

= e^{2 x} + e^{x} + 0

Simplify

= e^{x} + e^{2 x}

3 sin (4 x)

\frac{d}{d x} (x^{4} + cos (x) + 1)

\int \frac{( 16 - 9 x ^{2} ) ^{\frac{3}{2}}}{x ^{6}} d x

\int \frac{16}{( x + 2 ) ^{2}} d x

y^{^{'}} = y + x y

What is the derivative of y= 1/2 e^{2x}+e^x+1 ?
The derivative of y= 1/2 e^{2x}+e^x+1 is e^x+e^{2x}
What is the first derivative of y= 1/2 e^{2x}+e^x+1 ?
The first derivative of y= 1/2 e^{2x}+e^x+1 is e^x+e^{2x}